Fourth grade
1 answer:
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The length of AB is 9.
Solution:
Given data:
Radius OC = 8
Tangent AC = 15
The angle between the tangent and radius is always right angle.
∠C = 90°.
Hence OCA is a right triangle.
Using Pythagoras theorem,
<em>In a right triangle square of the hypotenuse is equal to the sum of the squares of the other two sides.</em>
Taking square root on both sides of the equation, we get
OA = 17
OB is the radius of the circle.
⇒ OB = 8
AB = OA – OB
= 17 – 8
= 9
AB = 9
Hence the length of AB is 9.
Answer:
2.55
Step-by-step explanation:
Draw a picture of the triangle formed by points P, A, and B. The angle of the line from P to A is 225°. The angle of the line from P to B is 116°. The angle of the line from B to A is 258°, and the length of the line is 3.91.
The easiest way to solve this is by first finding the angle of the line from B to P. Using interior angles, we can show that this is 180° − 116° = 64°.
Next, we can show that:
∠APB = 225° − 116° = 109°
∠ABP = 360° − (258° + 64°) = 38°
Finally, we can use law of sines to find AP.
AP / sin 38° = 3.91 / sin 109°
AP = 2.55
